Detroit won for the third time in nine games, while Miami lost for only the second time in eight.
Drummond had his fourth 20-rebound game of the season. Dwight Howard has recorded the only other one in the NBA this year.
Reggie Jackson added 18 points and seven rebounds for the Pistons, who had five players in double figures.
Gerald Green had 16 points for Miami, while Hassan Whiteside finished with 15 points and 13 rebounds. Dwyane Wade scored two points on 1-for-9 shooting -- the fewest points he has ever scored in at least 20 minutes of action.